Vi glæder os til premieren om to uger.

Because the usual Danish expression is at glæde sig til, which means to look forward to.

So this verb is normally used reflexively here:

• jeg glæder mig til = I’m looking forward to
• du glæder dig til = you’re looking forward to
• vi glæder os til = we’re looking forward to

The os matches the subject vi.

Without the reflexive pronoun, glæde usually has a different meaning, more like to please / to make someone happy.

Os means ourselves/us as a reflexive pronoun.

In English, we do not say we look ourselves forward, but Danish uses this reflexive structure:

• Vi glæder os til ...

So os is not extra; it is part of the normal pattern of the expression.

Here, til is part of the fixed expression glæde sig til.

You should learn it as one unit:

• glæde sig til + noun
  • Vi glæder os til premieren.
• glæde sig til + at + verb
  • Vi glæder os til at se filmen.

So til is required after glæde sig when you mean look forward to.

Because premieren is the definite form: the premiere.

Danish often adds the definite article to the end of the noun instead of using a separate word like the.

• en premiere = a premiere
• premieren = the premiere

So premieren already includes the meaning of the.

In Danish, the definite article is usually attached to the noun as a suffix.

So instead of saying something like the premiere, Danish says:

• premieren

This is very common in Danish:

• en film → filmen
• en bog → bogen
• en premiere → premieren

A separate definite word can appear in some other structures, especially with adjectives:

• den nye film = the new film

But in your sentence, premieren by itself is the normal form.

Om to uger means in two weeks.

Danish uses om + time period to mean after this amount of time / from now:

• om en time = in an hour
• om tre dage = in three days
• om to uger = in two weeks

This is different from i:

• i to uger = for two weeks

So:

• Vi ses om to uger = See you in two weeks
• Jeg har boet her i to uger = I have lived here for two weeks

Because Danish very often uses the present tense for future meaning when the context makes the time clear.

Here, om to uger already tells you that the event is in the future, so Danish does not need a special future form.

Compare:

• Vi glæder os til premieren om to uger.
• literally: We look forward to the premiere in two weeks

This is completely normal Danish.

In normal use, it is understood as referring to the time of the premiere: the premiere is in two weeks.

So the sentence means that there is a premiere coming up in two weeks, and we are looking forward to it now.

If you want to make that relationship extra clear, Danish can also say something like:

• Vi glæder os til premieren, som er om to uger.

But the original sentence is natural and idiomatic.

Then you normally use at + infinitive after til.

Examples:

• Jeg glæder mig til at se filmen. = I’m looking forward to seeing the film.
• Vi glæder os til at møde dem. = We’re looking forward to meeting them.

So:

• glæde sig til + noun
• glæde sig til + at + verb

That is a very useful pattern to remember.

Yes. At se frem til also means to look forward to.

Both are correct, but there is a slight difference in feel:

• glæde sig til = very common, natural, often a bit more warm or personal
• se frem til = also common, sometimes a bit more neutral or formal

So in everyday speech, Vi glæder os til premieren is extremely natural.

Yes, especially glæder.

A few points:

• glæ- has the Danish æ vowel, somewhat like the vowel in English cat, but not exactly.
• The d in glæder is usually a soft d, not a strong English d.
• premieren has the stress on the middle part: pre-mi-E-ren.

If you are just starting, the most important thing is to recognize the whole chunk:

• Vi glæder os til ...

That expression is worth learning as one unit, both in meaning and pronunciation.